2007/03/02 by Joachim Schröter, Schröter, Joachim
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0703013
23 pages, 1 figure
arxiv created 2007/03/02 · openalex publication_date 2007/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper (Part I of a series of three papers) an axiomatic formulation of GR is given, here use is made of the concept of pre-radar charts. These charts have "infinitesimally" the same properties as the true radar charts used in space-time theory. Their existence in GR has far-reaching consequences which are discussed throughout the papers. For the sake of simplicity and convenience I consider only such material systems the state of which is defined by a velocity field, a mass density and a temperature field. But the main results hold also for more complex systems. It follows from the axiomatics that the pre-radar charts define an atlas for the space-time manifold and that, in addition, they generate the metric, the velocity field and the displacement of the matter. Therefore, they are called generating functions. They act like "potentials". At the end of the paper it is shown that the existence of pre-radar charts allows to simplify the original axiomatics drasticly. But the two versions of GR are equivalent.